The two Cosmic Speeds

The speed needed to set a spacecraft into orbit just above the earth's surface.

$$ F_{\omega} = F_{g} $$$$ v = \sqrt{g_0 R_E} $$

The speed required to escape the gravitational field in order to never return.

$$ E_{kin} = E_{grav} $$$$ \frac{m v^2}{2} = G \frac{M m}{R_E} $$

Both assuming no friction

The orbital elements

a = the semi-major axis

e = the eccentricity

i = the inclination

$\Omega$ = the right ascension of the ascending node

$\omega$ = the argument of perigee

$\nu$ = the true anomaly (time varying)

Launch Windows

In rocket science, fuel calculation and savings are crucial to achiece a successfull mission. In order to launch directly into orbit, the launch site must be situated directly below the satellite orbit. By this, we may only launch satellites into orbits with higher inclination than the launch site's latitude.

$$ L_0 \leq i $$

Hohman Transfer

A Hohman transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

Different types of orbit

NASA mentiones about 11 standards types of orbits, but in this course the requirement is only to know of the four mentioned below and how they're used.

Geostationary orbit (GEO)

The concept of GEO is that the orbits around earth matching earth's sidereal rotation period. All geostationary orbits have a semi-major axis of 42164km, they stays exactly above the equator and it complete one full orbit of Earth per sidereal day.

Low Earth Orbit (LEO)

Geocentric orbits with altitudes from 160 to 2000km. This is the area where all manned spaceflights have taken place and where the ISS are located. Objects in LEO envounter atmospheric drag from tthe thermosphere or exosphere. The most common types of satelittes in this orbit is earth observation satellites as well as spy satellites.

Medium Earth Orbit (MEO)

Ranging in altitude from 2000km to just below 35786km and is also called inermediate circular orbit. These orbits usually have large inclination such that they covers most of the earth. Commonly used by navigation satellites.

Highly Elliptical Orbit (HEO)

This orbit is commonly percieved as High Earth Orbit. HEO are often known as Molniya orbits named after the Soviet communication satellites. Much of the area of the former Soviet Union and Russia is located at high latitudes. To broadcast to these latitudes from GEO would require considerable power due to low elevation angles. It also cost less energy to put into Molniya then GEO. The main disadvantage are that the ground station needs a steerable antenna to track the spacecraft and that it passes through the Van Allen belt four times a day.

Observation from Earth

Atmospheric Windows

The Atmospgeric windows is that portion of the electromagnetic spectrum that can be transmitted through the atmosphere without any distortion or absorption. Light in vertain wavelength regions can penetrate the atmosphere very well.

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Aperture

In norwegian: Blenderåpning

Angular and standard

The size of the aperture and the wavelength of radiation determines the smallest object we can see. In other words - the resolution.

The first equation is called the angular resolution, and the second only resolution. These concept of aperture is commonly used in both optics and radar. Resolution gives a lot of problems as the resolution is determined by the wavelength.

Synthetic

Synthetic aperture is used in the context of radars. A SAR is an imaging radar mounted on a moving platform. Electromagnetic waves are sequentially transmitted and reflected echoes are collected, digitized and stored by the radar antenna for later processing.

Note that the signal sent in the picture is a Chirp-signal.

Pulse Signal Detection

Navigation

The GPS satellite

Naviagation Signals

A standard navigation message is broadcasted at 50 bit/s over a period of 30 seconds giving a frame length of 1500 bits:

Ephemeris is data giving the satellite's precise orbit and is updated every 2 hour and valid for 4 hours. The Ephemeris is defined by 16 parameters which is broadcasted with high accuracy.

There are two characteristic transmitter frequencies:

L1: 1.57542 GHz

L2: 1.22760 GHz

The L1 frequency carries the navigation message and the Standard Positioning Service code signals. On the contrary, the L2 is used to measure the ionospheric delay by Precise Positioning Service equipped recievers.

The Atmosphere

The atmosphere is divided into multiple stages with gas or air as we know it, ranging from the ground and beyond into the skies. We divide into following "spheres":

Troposphere 0 - 8/15km

Stratosphere 15 - 50/60km

Mesosphere 60 - 95/120km

Termosphere 120 - 600km

Exosphere 600 - beyond

There is also a region stretching from the mid-Troposphere and beyond also known as the Ionosphere. This is the region of the atmosphere being ionized by solar radiation and it's also responsible for the Aurora Borealis. As you see in the listing, there are some kind of undecided where the different layers end, this is due to the different "pauses" in between the layers.

The layer we probably know the most of already is the troposphere. This is the so called planetary boundary layer and where all weather is taking place. The troposphere can be compared with the turbulent and laminar area around a surface where fluid flows. Though are clouds as we know it one of the most difficult fields in physics. As a physicist says it: Cloud droplets or crystals are macroscopic, and they cannot be understood without the knowledge of the microscopic. The whole troposphere is a result of global wind systems, planetary waves, energy balance, aerosol and reflection of sun rays.

Troposphere

Stratosphere

Mesosphere

Ionosphere

Satellite Platforms

Requirements

In order to launch a satellite there are a lots of requirements that is neccessary to fulfill before being ready and also a lot of things to take into consideration. Examples are requirementsof how to be linked to the mission of the satellite, how to being able to operate in the hostile space environment, how long to operate, hwo to keep orobit and orientation, how to keep contact, cost estimation and how to control the satellite after its death.

Mass Control

It has been sais that the more sophisticated the satellite is, the longer development time, and more things can go wrong. The insurance price increases to a level out of proportions or it may even become impossible to insure. The mass to launch is extremely important and we will see some of the different aspects here.

If we break down the dry mass of a satellite we have approximately following

Battery 15%

Solar Array 11%

Payload 31%

Rest 43% (thrusters etc.)

Rocket Equation

The forces on a rocket change dramatically during a typical flight. This figure shows a derivation of the change in velocity during powered flight while accounting for the changing mass of the rocket. During powered flight the propellants of the propulsion system are constantly being exhausted from the nozzle. As a result, the weight of the rocket is constantly changing. In this derivation, we are going to neglect the effects of aerodynamic lift and drag.

Fuel and Payload

Due to today's propulsion systems, we cannot achieve any of the cosmic speed even without payload.

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Attitude and orbital control

Attitude defines a vehicle's orientation in space and it is controlled by the ADCS, which is "Attitude Determination and Control Subsystem". The desired attitude of a satellite depends on it mission and what to achieve.

We have a lot of different factors and orbital perturbations which can cause wrong attitude and orbit. These factors can be

Atmospheric friction

Irregulatities of the earth gravitational field

Lunar and solar gravity

Solar pressure

These different factors creates different torques which can make it spin out of orbit etc. There are different ways to stabilize a satellite due to change in torque and forces working on the satellite:

In order to be able to detect irregularities in attitude and orbit, we need sensors and reference systems. Some examples are sun sensors, earth sensor, star sensor and gyroscopic sensors.

Power Control

It is usually the available power that will be determinant for the satellite's lifetime and performance, not the ageing of structure or materials. Fuel is commnly used for orbital control, from launch, correction manouvers to the graveyard. Solar panels is the most common power supply for electronics and for continous operation.

Ionic propellant
- Acceleration of positive ions
- Complicated construction, reliable and stable
- Can be stopped once ignited and restartable
- High $I_{sp}$ and very low thrust

Ionic propellant are mostly still being developed and is mainly used for providing thrust on longer missions after escaped gravity. There are also alot of research these days concerning a mixture of both solid and liquid propellant. The norwegian company "Nammo" is currently working a lot on these types of engines.

Illustration of a rocket engine based on liquid propellant. Picture brought from NASA.

Telemetry, tracking and command

The main communication channel between earth and the satellite is the ground control centre. A satellite operator or control centre needs to monitor and operate all the control system such as solar panels, temperature, orbital corrections, orientation of antennas, transmitting power and maneuvers to avoid impacts with to much ionization as well as debris and sun storms. It may also require telemetry in order to execute updates, bug correction and traffic monitoring.

Thermal Control

Mechanical

Debris

Debris as "space trash" is a continously growing problem. As of this day, about 12500 larger pieces of debris is orbiting earth and it is assumed that there are about 600.000 pieces large enough to make serious damage. The debris is mostly coming from old and no longer operative satellites and other space equipment. The problem is still increasing in a time of more and more activity around the earth.

Microgravity

Microgravity is the condition based on very low levels of gravity working on the body or other masses and it's mainly from below $ 10^{-4} g$ that we are used to on earth.